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A coupled distributed lagrange multiplier (DLM) and discrete element method (DEM) approach to simulate particulate flow with collisions

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POWDER TECHNOLOGY 2022年 398卷 117091-117091页

作者： Sharma, Govind Nangia, Nishant Ray, Bahni Bhalla, Amneet Pal Singh Indian Inst Technol Delhi Dept Mech Engn New Delhi India San Diego State Univ Dept Mech Engn San Diego CA 92182 USA

In this paper, a coupled DLM-DEM numerical approach is proposed to enable particle-particle and particle-wall interactions within the open-source IBAMR (Immersed Boundary Adaptive Mesh Refinement) framework. A soft-sphere DEM collision model is adopted and compared against the particle-particle repulsion force model suggested in the literature. It is demonstrated that the former collision model remains effective at both low and high particle-fluid density ratios, whereas the latter model can lead to unphysical particle-particle interac-tion dynamics at high density ratios. Moreover, the soft-sphere DEM collision model is based on physical material properties, which is in contrast to an artificial parameter-based repulsion force model. The proposed DLM-DEM approach is validated by simulating the particle-particle collision in drafting, kissing, and tumbling (DKT) phe-nomenon, and particle-wall collision at various Stokes numbers. Using this approach, we also simulate the inter-actions between a single colliding particle and a particle cluster and analyze the particles' motion and distribution. Additionally, sedimentation of polygon-shaped particles is also considered to demonstrate the ver-satility of the proposed approach.(c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Fluid-particle interaction distributed lagrange multiplier method Soft-sphere DEM collision Immersed boundary method Particle-particle cluster interactions

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Three dimensional fluid-structure interaction under pulsatile flow by using distributed lagrange multiplier method

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MATHEMATICAL AND COMPUTER MODELLING 2011年第1-2期53卷 21-41页

作者： Pati, Arati Nanda Ladipo, Kehinde Paniagua, David Glowinski, Roland Univ Houston Dept Math Houston TX 77204 USA Univ Ontario Fac Sci Inst Technol Oshawa ON L1H 7K4 Canada Baylor Coll Med Houston TX 77030 USA

In this article we discuss an application of a lagrange multiplier based fictitious domain method for the simulation of moving leaflets in an unsteady flow generated by pressure gradients during the systolic phase of the cardiac cycle in three dimensional geometry. The mathematical model includes the Navier-Stokes equations coupled with the Euler-Newton equations describing fluid-structure interaction for the generalized Neumann boundary conditions on upstream and downstream boundaries. The solution method includes the finite element method combined with an operator-splitting scheme, where the fictitious formulation allows the flow calculations to be in a fixed rectangular parallelepiped to predict the dynamic structural positions and flow field during the valve opening and closing phases. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： distributed lagrange multiplier method Fluid-structure interaction Pulsatile flow

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A versatile implicit iterative approach for fully resolved simulation of self-propulsion

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2010年第37-40期199卷 2417-2424页

作者： Curet, Oscar M. AlAli, Ibrahim K. MacIver, Malcolm A. Patankar, Neelesh A. Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Stanford Univ Dept Mech Engn Stanford CA 94305 USA Northwestern Univ Dept Biomed Engn Evanston IL 60208 USA Northwestern Univ Dept Neurobiol & Physiol Evanston IL 60208 USA

We present a computational approach for fully resolved simulation of self-propulsion of organisms through a fluid A new implicit iterative algorithm is developed that solves for the swimming velocities of the organism with prescribed deformation kinematics A solution for the surrounding flow field is also obtained This approach uses a constraint-based formulation of the problem of self-propulsion developed by Shirgaonkar et al. [1]. The approach in this paper is unlike the previous work [1] where a fractional time stepping scheme was used. Fractional time stepping schemes, while efficient for moderate to high Reynolds number problems, are not suitable for zero or low Reynolds number problems where the inertia term in the governing equation is absent or negligible In such cases the implicit iterative algorithm presented here is more appropriate We validate the method by simulating self-propulsion of bacterial flagellum, jellyfish (Aurelia aurita), and larval zebrafish (Danio rerio) Comparison of the computational results with theoretical and experimental results for the test cases is found to be very good. (C) 2010 Elsevier B V. All rights reserved

关键词： Self-propulsion Biolocomotion DNS Fully resolved simulation (FRS) Immersed boundary method distributed lagrange multiplier method

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A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion

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JOURNAL OF COMPUTATIONAL PHYSICS 2009年第7期228卷 2366-2390页

作者： Shirgaonkar, Anup A. Maciver, Malcolm A. Patankar, Neelesh A. Northwestern Univ Robert R McCormick Sch Engn & Appl Sci Dept Mech Engn Evanston IL 60208 USA Northwestern Univ Robert R McCormick Sch Engn & Appl Sci Dept Biomed Engn Evanston IL 60208 USA

We present a computational algorithm for fully resolved numerical simulation (FRS) of rigid and deforming bodies moving in fluids. Given the deformation of the body in its own reference frame, the method solves for the swimming velocity of the body together with the surrounding flow field, and the hydrodynamic forces on the body. We provide the mathematical foundation of the algorithm based on distributed lagrange multipliers, and show that it naturally connects with vortex methods through a vorticity source at the interface. We demonstrate applications to rigid and flexible bodies, membranes, and bodies with a propelling membrane attached to them. In contrast to some existing methods, the swimming velocity of the body is not prescribed but is computed along with the forces, without requiring a body-fitted grid. The algorithm is designed to be fast, efficient, and easy to implement in existing fluid dynamics codes for practical solid-fluid problems in engineering and biology. (C) 2008 Elsevier Inc. All rights reserved.

关键词： Self-propulsion Biolocomotion DNS Fully resolved simulation (FRS) Immersed boundary method distributed lagrange multiplier method

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Fictitious versus nonfictitious formulation of backward step flow

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MATHEMATICAL AND COMPUTER MODELLING 2008年第1-2期47卷 72-91页

作者： Pati, Arati Nanda Univ Houston Dept Math Houston TX 77204 USA

In this article we discuss the numerical results obtained by two methods to solve the incompressible viscous flow modelled by the Navier-Stokes equations for a backward step flow for Reynold's number Re = 50. In the first method we have used a nonfictitious formulation of the problem and compared the result with the alternating direction method obtained by Glowinski. In the second method we have considered the fictitious formulation of the same problem based on the distributed lagrange multiplier method. Our goal is to observe its behavior at the nonsmooth points, both with matching and nonmatching boundary points. In the fictitious formulation the step is treated as a nonmoving obstacle present in a channel by extending the flow region to a simplified rectangular domain. In this study, we find that our results compare very well for this stationary problem with nonsmooth boundary. Our solution method combines the finite element method and the operator splitting scheme of the Marchuk-Yanenko type. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： backward step fictitious formulation distributed lagrange multiplier method Marchuk-Yanenko splitting scheme

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Fluid-structure interaction for a pressure driven flow

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MATHEMATICAL AND COMPUTER MODELLING 2008年第1-2期47卷 1-26页

作者： Pati, Arati Nanda Univ Houston Dept Math Houston TX 77204 USA

In this article we discuss the application of a lagrange multiplier based fictitious domain method for the simulation of the motion of two rigid flaps in an unsteady flow generated by pressure gradients. The distributed lagrange multiplier technique can be an important numerical tool to design a mechanical heart valve and investigate the flow around rigid flaps without assuming the motion of the flaps in advance. Here, we derive a mathematical formulation of a fluid-structure interaction model that includes the generalized Neumann boundary conditions on the upstream and downstream boundaries along with rigid flaps rotating around the fixed points. The solution method includes the finite element approximation for space and the Marchuk-Yanenko operator splitting scheme for time discretization. This study presents the numerical results obtained for flap motion for a simple sinusoidal wave. Furthermore, these simulations are extended to apply to a more complex biological system involving the systolic phase of the pulse pressure. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： distributed lagrange multiplier method Marchuk-Yanenko splitting scheme fluid-structure interaction pulse pressure

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Manipulation of particles using dielectrophoresis

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MECHANICS RESEARCH COMMUNICATIONS 2006年第1期33卷 108-122页

作者： Kadaksham, J Singh, P Aubry, N New Jersey Inst Technol Dept Mech Engn Newark NJ 07102 USA

A numerical scheme based on the distributed lagrange multiplier method (DLM) is used to study the motion of particles of electrorheological suspensions subjected to non-uniform electric fields. At small Reynolds number, the time taken by the particles to collect at the minimums or maximums of the electric field is primarily determined by a parameter defined to be the ratio of the dielectrophoretic and viscous forces. Simulations show that in non-uniform electric fields the collection time is also influenced by a parameter defined by the ratio of the electrostatic particle-particle interaction and dielectrophoretic forces. The collection time decreases as this parameter decreases because when this parameter is less than one, particles move to the regions of high or low electric field regions individually. However, when this parameter is greater than one, particles regroup into chains which then move toward the electric field maximums or minimums without breaking. It is also shown that when the real part of the Clausius-Mosotti factor (beta) is negative the positions of the local minimums of the electric field, and thus also the locations where particles collect, can be modified by changing the electric potential boundary conditions. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： dielectrophoresis electrorheological suspensions finite-element method direct numerical simulations distributed lagrange multiplier method

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Direct numerical simulation of the Brownian motion of particles by using fluctuating hydrodynamic equations

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JOURNAL OF COMPUTATIONAL PHYSICS 2004年第2期201卷 466-486页

作者： Sharma, N Patankar, NA Northwestern Univ Dept Mech Engn Evanston IL 60208 USA

In this paper, we present a direct numerical simulation scheme for the Brownian motion of particles. In this approach, the thermal fluctuations are included in the fluid equations via random stress terms. Solving the fluctuating hydrodynamic equations coupled with the particle equations of motion result in the Brownian motion of the particles. There is no need to add a random force term in the particle equations. The particles acquire random motion through the hydrodynamic force acting on its surface from the surrounding fluctuating fluid. The random stress in the fluid equations are easy to calculate unlike the random terms in the conventional Brownian dynamics type approaches. We present a three-dimensional implementation along with validation. (C) 2004 Elsevier Inc. All rights reserved.

关键词： fluctuating hydrodynamics mesoscopic scale Brownian motion micro/nanoscale computational fluid dynamics direct numerical simulation distributed lagrange multiplier method control volume method

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